CINCINNATI – Carlos Dunlap and Geno Atkins have raced each other thousands of times over the last eight seasons. Sometimes Dunlap wins. Sometimes Atkins does. Occasionally they tie, arriving at the quarterback at the same time and end up splitting a sack.

Tuesday afternoon, Dunlap and Atkins ended a longer race in another dead heat, only this time they ended up splitting $110 million in what was one of the biggest days in franchise history for the front office.

“You don’t get many chances to sign two Pro Bowl defensive linemen in one day,” said Bengals Vice President Troy Blackburn, who negotiated Dunlap’s three-year, $45 million extension with agent Drew Rosenhaus while Executive Vice President Katie Blackburn worked Atkins’ four-year, $65.2 million deal with agent Pat Dye.

“We’ve been talking to these guys all offseason,” Katie Blackburn said, noting that talks began in February at the combine. “A lot of stuff depends on what...